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BELL SYSTEM TECHNICAL JOURNAL 



figure that both the upper and lower limits of audibility which are 

 found in any particular experimental investigation will very largely 

 depend upon the intensity of the tones sounded. For example, 

 if the intensity were along the .01 dyne line, the limits would be 

 200 and 12,600 cycles. 



The area enclosed between the maximum and minimum audibility 

 curves has been called the auditory-sensation area and each point 

 in it represents a pure tone. The question then arises: How many 

 such pure tones can be sensed by the normal ear? 



The answer to this question has been made possible by the recent 

 work of Mr. V. O. Knudsen. 14 In this work Knudsen made determi- 

 nations of the sensibility of the ear for small differences in pitch and 

 intensity. In Fig. 2, the average results of his measurements for 



Minimum Perceptible Difference in Intensity 



aE 



10 20 30 40 50 60 10 80 90 100 110 



Loudness of the Tone 

 Fig. 2 



changes in intensity are shown. Each ordinate gives the fractional 

 change in the sound energy which is just perceptible, this fractional 

 change being called the Fechner ratio. The abscissae are equal to 

 ten times the logarithm of the ratio of intensities, the zero corre- 



